German Patent Application No. DE 10 2010 040097 A1 describes a braking system for motor vehicles that can be activated both by the vehicle driver and independently of the vehicle driver. The braking system described has, inter alia, an electrohydraulic pressure furnishing device that delivers a braking system pressure, as well as a pressure modulation unit that has, for each wheel brake, an inlet valve as well as an outlet valve for establishing individual-wheel brake pressures. In order to avoid inconvenience to the vehicle driver in particular in the event of a failure of the electrical system of the motor vehicle, it is proposed according to the invention that switch-in valves electrically actuatable for each circuit be interposed between the pressure furnishing device and the pressure modulation unit, which valves, in an activated state, create a hydraulic connection between the pressure furnishing device and the pressure modulation unit.